A082207 Palindromes whose product of digits is a positive palindrome.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 222, 313, 676, 777, 1111, 1221, 1331, 2112, 3113, 11111, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911, 12121, 12221, 13131, 16761, 17771, 21112, 21212

Offset: 1

Author

Amarnath Murthy, Apr 10 2003

Keywords

• base
• easy
• nonn

Comments

The unary sequence A000042 is a trivial subsequence.

Conjecture: There are infinitely many terms in the sequence (of the type 777) for which the product of digits > 10.

Subset of A117055, containing terms for which product of digits is greater than 0. - Jayanta Basu, May 15 2013

Examples

			777 is a term as 7^3 = 343 is a palindrome.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..89 (all terms up to 10 million)

Crossrefs

Cf. A082208.

Programs

Mathematica

id[n_]:=IntegerDigits[n]; palQ[n_]:=Reverse[x=id[n]]==x; t={}; Do[If[palQ[n] && (y=Times@@id[n]) > 0 && palQ[y], AppendTo[t,n]], {n,21220}]; t (* Jayanta Basu, May 15 2013 *)
Select[Range[22000],FreeQ[IntegerDigits[#],0]&&AllTrue[{#,Times @@ IntegerDigits[ #]},PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 22 2019 *)

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003